Mensuration Test

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Mensuration Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct formula for surface area of a cylinder.

A
$$\displaystyle 2\pi { r }^{ 2 }+2\pi rh$$

B
$$\displaystyle \pi { r }^{ 2 }+\pi rh$$

C
$$\displaystyle 2\pi r+2\pi rh$$

D
$$\displaystyle 2\pi { r }^{ 2 }+\pi rh$$

Solution

A cylinder comprises two circles and one rectangle as given in the figure
The surface area of a circle is $$\pi r^2$$ where $$r$$ is the radius and the surface area of a rectangle is $$2\pi rh$$.
$$\implies$$ Surface area of cylinder $$=2\times$$ area of the circular base $$+$$ area of the rectangle
$$\Rightarrow $$ Surface area of cylinder $$=2\pi r^2+2\pi rh$$
Question 2
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Find the height of a cylinder that has a diameter of $$10$$ feet and a surface area of $$\displaystyle 220{\ ft }^{ 2 }$$. Round your answer to the nearest whole number.
(use $$\displaystyle \pi ={ 22 }/{ 7 }$$).

A
$$0.1$$ ft

B
$$3$$ ft

C
$$2$$ ft

D
$$1$$ ft

Solution

Surface area of cylinder is $$A=2πr(r+h)$$
Here the cylinder has surface area $$A=220$$ ft$$^2$$ and diameter $$10$$ ft and therefore, the radius is half of the diameter that is$$r=5$$ ft.
Thus,
$$A=2πr(r+h)\\ \Rightarrow 220=2\times \frac { 22 }{ 7 } \times 5(5+h)\\ \Rightarrow 220=\frac { 44 }{ 7 } (25+5h)\\ \Rightarrow 220\times 7=1100+220h\\ \Rightarrow 1540-1100=220h\\ \Rightarrow 220h=440\\ \Rightarrow h=\frac { 440 }{ 220 } =2$$
Hence, the height of the cylinder is $$2$$ ft.
Question 3
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A cylindrical drum has its height 20 inches and curved surface area as $$\displaystyle 200{ in }^{ 2 }$$. Find surface area of cylindrical drum.($$\displaystyle \pi ={ 22 }/{ 7 }$$)

A
$$\displaystyle 203.5{ in }^{ 2 }$$

B
$$\displaystyle 207.3{ in }^{ 2 }$$

C
$$\displaystyle 215.7{ in }^{ 2 }$$

D
$$\displaystyle 218.13$$

Solution
Question 4
1 / -0

Judah wants to make a cylindrical drum that will fit a bass with a height $$15 $$in. and a diameter of $$48$$ in. What is the surface area of the drum?
Take $$\pi = 3.14$$

A
$$\displaystyle 5810.10in$$

B
$$\displaystyle 5810.10{ in }^{ 2 }$$

C
$$\displaystyle 5878.08{ in }^{ 2 }$$

D
$$\displaystyle 5878{ in }^{ 2 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here, diameter is $$48$$ in and therefore, the radius is half of diameter that is $$r=24$$ in and the height is $$h=15$$ in.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 24(24+15)=150.72\times 39=5878.08$$

Hence, the surface area of the cylindrical drum is $$5878.08$$ in$$^2$$.
Question 5
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Find the total surface area of the cylinder. (Use $$\displaystyle \pi =3.14$$).

A
$$\displaystyle 678.99{ ft }^{ 2 }$$

B
$$\displaystyle 3881.05{ ft }^{ 2 }$$

C
$$\displaystyle 3881.04ft$$

D
$$\displaystyle 678.24{ ft }^{ 2 }$$

Solution

Given: $$r=6ft$$ and $$h=12ft$$
The total surface area of a cylinder = $$\displaystyle 2\pi r\left( r+h \right) $$
$$\displaystyle =2\times 3.14\times 6\left( 6+12 \right) $$
$$\displaystyle =2\times 3.14\times 6\left( 18 \right) $$
$$=\displaystyle 678.24{ ft }^{ 2 }$$

So, option D is correct.
Question 6
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The surface area of a cylindrical box is $$\displaystyle 132\ { mm }^{ 2 }$$ and its height is $$4 \ mm.$$ Find its radius.

A
$$\displaystyle 2 $$ $${ mm }$$

B
$$\displaystyle 3 $$ $${ mm }$$

C
$$\displaystyle 4 $$ $${ mm }$$

D
$$\displaystyle 5 $$ $${ mm }$$

Solution

Given: Cylindrical box has surface area $$A=132$$ $$mm^2$$ and height $$h=4\ mm$$

We know surface area of cylinder is $$A=2πr(r+h)$$

Thus, $$ 132=2\times \dfrac { 22 }{ 7 } \times r(r+4)$$

$$ \Rightarrow 132=\dfrac { 44 }{ 7 } r(r+4)$$

$$ \Rightarrow 132\times 7=44r(r+4)$$

$$\Rightarrow 924=44r^{ 2 }+176r$$

$$\Rightarrow 44r^{ 2 }+176r-924=0$$

$$ \Rightarrow r^{ 2 }+4r-21=0$$

$$ \Rightarrow r^{ 2 }+7r-3r-21=0$$

$$ \Rightarrow r(r+7)-3(r+7)=0$$

$$ \Rightarrow r+7=0,\quad r-3=0$$

$$ \Rightarrow r=-7,\quad r=3$$

Hence, the radius of the cylindrical box is $$3$$ mm.
Question 7
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A skating board rocks back and forth on a wooden cylinder. The cylinder has a radius of 6 inches and a surface area is $$\displaystyle 590{ in }^{ 2 }$$. Find the height of the cylinder. ($$\displaystyle \pi =3.14$$).

A
$$10$$ in

B
$$9.65$$ in

C
$$9$$ in

D
$$9.5$$ in

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here the wooden cylinder has surface area $$A=590$$ in$$^2$$ and radius $$r=6$$ mm.

Thus,

$$A=2πr(r+h)\\ \Rightarrow 590=2\times \dfrac { 22 }{ 7 } \times 6(6+h)\\ \Rightarrow 590=\dfrac { 44 }{ 7 } (36+6h)\\ \Rightarrow 590\times 7=1584+264h\\ \Rightarrow 4130-1584=264h\\ \Rightarrow 264h=2546\\ \Rightarrow h=\dfrac { 2546 }{ 264 } =9.643$$

Hence, the height of the wooden cylinder is $$9.65$$ in.
Question 8
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David built a recycling cylindrical bin that is 12 feet long and its base is 56 feet radius. Find the surface area of the bin.

A
$$\displaystyle 23936{\ ft }^{ 3 }$$

B
$$\displaystyle 23936{\ ft }^{ 2 }$$

C
$$\displaystyle 23950{ \ ft }^{ 2 }$$

D
$$\displaystyle 23936\ ft$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here the cylindrical bin has radius $$r=56$$ ft and height $$h=12$$ ft.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 56(56+12)=351.68\times 68=23936.24$$

Hence, the surface area of the cylindrical bin is approximately equal to $$23936$$ ft$$^2$$.
Question 9
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A gas cylinder has a diameter of $$14 $$m and height is $$0.2$$m. Find its surface area. ($$\displaystyle \pi ={ 22 }/{ 7 }$$)

A
$$\displaystyle 316.512{ mm }^{ 2 }$$

B
$$\displaystyle 316.512m$$

C
$$\displaystyle 316.512{ m }^{ 3 }$$

D
$$\displaystyle 316.512{ m }^{ 2 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$
Here the gas cylinder has diameter $$14$$ m and therefore, the radius is half of diameter that is $$r=7$$ m and height $$h=0.2$$ m.
Thus,
$$A=2πr(r+h)=2 \times \dfrac {22}{7}\times 7(7+0.2)=316.512$$
Hence, the surface area of the gas cylinder is $$316.512m^2$$.
Question 10
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The curved surface area of a cylinder is $$\displaystyle 188.4\ { m }^{ 2 }$$. The height is $$12\ m$$. What is the radius? (use$$\displaystyle \pi =3.14$$).

A
$$\displaystyle 2\ { cm }$$

B
$$\displaystyle 2.5\ cm$$

C
$$\displaystyle 2\ m$$

D
$$\displaystyle 2.5\ m$$

Solution

Curved surface area of cylinder is $$A=2πrh$$

Here, the curved surface area is $$A=188.4\ m^2$$ the height is $$h=12\ m$$.

Thus,

$$A=2πrh\\ \Rightarrow 188.4=2\times 3.14\times r\times 12\\ \Rightarrow 188.4=75.36r\\ \Rightarrow r=\dfrac { 188.4 }{ 75.36 } =2.5$$

Hence, radius of the cylinder is $$2.5\ m$$

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Mensuration Test - 27

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Mensuration Test - 27

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Question 1

$$\displaystyle 2\pi { r }^{ 2 }+2\pi rh$$

$$\displaystyle \pi { r }^{ 2 }+\pi rh$$

$$\displaystyle 2\pi r+2\pi rh$$

$$\displaystyle 2\pi { r }^{ 2 }+\pi rh$$

Solution

Question 2

$$0.1$$ ft

$$3$$ ft

$$2$$ ft

$$1$$ ft

Solution

Question 3

$$\displaystyle 203.5{ in }^{ 2 }$$

$$\displaystyle 207.3{ in }^{ 2 }$$

$$\displaystyle 215.7{ in }^{ 2 }$$

$$\displaystyle 218.13$$

Solution

Question 4

$$\displaystyle 5810.10in$$

$$\displaystyle 5810.10{ in }^{ 2 }$$

$$\displaystyle 5878.08{ in }^{ 2 }$$

$$\displaystyle 5878{ in }^{ 2 }$$

Solution

Question 5

$$\displaystyle 678.99{ ft }^{ 2 }$$

$$\displaystyle 3881.05{ ft }^{ 2 }$$

$$\displaystyle 3881.04ft$$

$$\displaystyle 678.24{ ft }^{ 2 }$$

Solution

Question 6

$$\displaystyle 2 $$ $${ mm }$$

$$\displaystyle 3 $$ $${ mm }$$

$$\displaystyle 4 $$ $${ mm }$$

$$\displaystyle 5 $$ $${ mm }$$

Solution

Question 7

$$10$$ in

$$9.65$$ in

$$9$$ in

$$9.5$$ in

Solution

Question 8

$$\displaystyle 23936{\ ft }^{ 3 }$$

$$\displaystyle 23936{\ ft }^{ 2 }$$

$$\displaystyle 23950{ \ ft }^{ 2 }$$

$$\displaystyle 23936\ ft$$

Solution

Question 9

$$\displaystyle 316.512{ mm }^{ 2 }$$

$$\displaystyle 316.512m$$

$$\displaystyle 316.512{ m }^{ 3 }$$

$$\displaystyle 316.512{ m }^{ 2 }$$

Solution

Question 10

$$\displaystyle 2\ { cm }$$

$$\displaystyle 2.5\ cm$$

$$\displaystyle 2\ m$$

$$\displaystyle 2.5\ m$$

Solution

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